The present disclosure relates to lithographic methods, and particularly to a method for generating a plurality of optimized wavefronts for a lithography process.
Printing state-of-the-art circuit patterns with available image-forming technology poses an important challenge for the semiconductor industry. For production costs to be viable the images must be formed with radiation whose wavelength is compatible with practical lenses (for example refractive lenses), and this limits the fundamental resolution of the image. It then becomes desirable to optimize the patterns on the masks which the imaging lenses project on the wafer as a means of forming the circuit pattern image, in order that the available resolution be exploited as fully as possible.
In the case where a single mask is projected to a wafer to form the circuit image (in a particular level), A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. K. Wong, “Optimum Mask and Source Patterns to Print a Given Shape,” JM3 1, no. 1 (2002): p. 13, which is incorporated herein by reference, shows that a suitably patterned mask can be obtained by first determining the optimum set of image forming waves that should be diffracted from the mask under irradiation by the (shaped) illumination source, and then designing manufacturable mask shapes to produce these diffracted waves. The problem of determining the optimal image-forming waves to diffract from the mask is a challenging one because it involves non-convex constraints in a high-dimensioned solution space, with the nominal scaling of the problem difficulty being exponential in the number of dimensions. Further, it has been shown that for a single advanced mask (in particular a phase-shift mask) the dimensionality can be reduced by first solving an averaged version of the problem to reduce the dimensionality, and then applying heuristics to find the solution within the reduced space.
A drawback to this prior-art method is that the shaped illumination source must illuminate all patterns in the mask, implying that those features in the shaped illumination source which are only well-suited to printing a limited subset of the desired circuit features must nonetheless illuminate all patterns in the mask, including those associated with high-quality printing of other mask features. The shapes in the illumination source pattern must then be chosen as a compromise.
It is known in the art that where general lithographic imaging is concerned, one can improve the quality of the circuit image by dividing the source shapes and mask shapes into two or more separate exposures (applied sequentially), so that after the mask shapes have been deployed across separate masks, each appropriate subset of the source shapes need only expose a mask which includes mask patterns that the subset of source shapes is well-suited to project, with other mask patterns being deployed to masks exposed by other subsets of the source shapes. For example, a technique known as double exposure in the art employs two separate sequential exposures of the same photoresist layer using two different photomasks. Double exposure allows the decomposition of two-dimensional patterns into two patterns which are easier to print. When two masks are used each individual mask has more space available to deploy enlarged serifs and assisting structures that aid printing. Although the use of multiple masks is costly, the practice has now become accepted (within limits) because of the extreme difficulty in printing the patterns for state-of-the-art circuits.
However, a drawback of the multiple mask approach is that the use of multiple masks increases the dimensionality of the mask design problem (in proportion to the number of masks used), or equivalently it increases the number of degrees of freedom which should be optimally exploited when determining the diffracted wavefronts from the two or more masks. Sub-optimal heuristics are often accepted that shirk optimization of the expanded degrees of freedom, through a process known as pattern decomposition. Pattern decomposition uses pre-assignment to decompose the multiple exposure back to a set of separated single exposures, for example using the heuristic of pre-assigning horizontally oriented features to an exposure with one source, and vertically oriented features to exposure with another.
In addition, modern circuit features are so fine that it can be desirable to use masks of the simplest kind, such as masks whose patterns consist of simple apertures in a comparatively thin set of opaque films, because the more complex mask topographies that are needed to support more advanced mask functionalities like phase-shifting can in practice introduce severe distortions with features of such extreme fineness. Although it is known that the optimal phase-shifted wavefront may (with a single mask, in the prior art) be obtainable from a space of reduced dimensionality, that reduced space may be too severely restricted to provide useful wavefronts from a mask that cannot employ phase shift.
In addition, when determining the imaging wavefronts it is preferable to take into account the possible positioning errors that can occur when exposures are superposed in a multiple exposure process, and this adds an additional complication to the problem.
Multiple exposure is well-known as a general technique for exposing wafers. Most steps of source mask optimization (“SMO”) for single exposure can be extended to multiple exposures in a fairly straightforward way, except for mask optimization, which on its face is more difficult to carry out optimally with more than one exposure.